NMMD: Efficient Cryo-EM Flexible Fitting Based on Simultaneous Normal Mode and Molecular Dynamics atomic displacements

Atomic models of cryo electron microscopy (cryo-EM) maps of biomolecular conformations are often obtained by flexible fitting of the maps with available atomic structures of other conformations (e.g., obtained by X-ray crystallography). This article presents a new flexible fitting method, NMMD, which combines normal mode analysis (NMA) and molecular dynamics simulation (MD). Given an atomic structure and a cryo-EM map to fit, NMMD simultaneously estimates global atomic displacements based on NMA and local displacements based on MD. NMMD was implemented by modifying EMfit, a flexible fitting method using MD only, in GENESIS 1.4. As EMfit, NMMD can be run with replica exchange umbrella sampling procedure. The new method was tested using a variety of EM maps (synthetic and experimental, with different noise levels and resolutions). The results of the tests show that adding normal modes to MD-based fitting makes the fitting faster (40% in average) and, in the majority of cases, more accurate.     

Symmetry-restrained flexible fitting for symmetric EM maps

Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems.     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

Cryo-electron microscopy (cryo-EM) has been widely used to explore conformational states of large biomolecular assemblies. The detailed interpretation of cryo-EM data requires the flexible fitting of a known high-resolution protein structure into a low-resolution cryo-EM map. To this end, we have developed what we believe is a new method based on a two-bead-per-residue protein representation, and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified elastic network model energy with a cryo-EM-fitting score and a collision energy that penalizes steric collisions. Unlike previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled. We have validated our method for a diverse set of 10 pairs of protein structures using simulated cryo-EM maps with a range of resolutions and in the absence/presence of random noise. We have shown that our method is both accurate and efficient compared with alternative techniques, and its performance is robust to the addition of random noise. Our method is also shown to be useful for the flexible fitting of three experimental cryo-EM maps.     

Flexible fitting of high-resolution x-ray structures into cryoelectron microscopy maps using biased molecular dynamics simulations

A methodology for flexible fitting of all-atom high-resolution structures into low-resolution cryoelectron microscopy (cryo-EM) maps is presented. Flexibility of the modeled structure is simulated by classical molecular dynamics and an additional effective potential is introduced to enhance the fitting process. The additional potential is proportional to the correlation coefficient between the experimental cryo-EM map and a synthetic map generated for an all-atom structure being fitted to the map. The additional forces are calculated as a gradient of the correlation coefficient. During the molecular dynamics simulations under the additional forces, the molecule undergoes a conformational transition that maximizes the correlation coefficient, which results in a high-accuracy fit of all-atom structure into a cryo-EM map. Using five test proteins that exhibit structural rearrangement during their biological activity, we demonstrate performance of our method. We also test our method on the experimental cryo-EM of elongation factor G and show that the model obtained is comparable to previous studies. In addition, we show that overfitting can be avoided by assessing the quality of the fitted model in terms of correlation coefficient and secondary structure preservation.     

Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM

A new method for the flexible fitting of high-resolution structures into low-resolution maps of macromolecular complexes from electron microscopy has been recently described in applications to simulated electron density maps. This method uses a linear combination of low-frequency normal modes in an iterative manner to deform the structure optimally to conform to the low-resolution electron density map. Gradient-following techniques in the coordinate space of collective normal modes are used to optimize the overall correlation coefficient between computed and measured electron densities. With this approach, multi-scale flexible fitting can be performed using all-atoms or Calpha atoms. In this paper, illustrative studies of normal mode based flexible fitting to experimental cryo-EM maps are presented for three different systems. Large, functionally relevant conformational changes for elongation factor G bound to the ribosome, Escherichia coli RNA polymerase and cowpea chlorotic mottle virus are elucidated as the result of the application of NMFF from high-resolution structures to cryo-electron microscopy maps.     

Finding rigid bodies in protein structures: Application to flexible fitting into cryoEM maps

We present RIBFIND, a method for detecting flexibility in protein structures via the clustering of secondary structural elements (SSEs) into rigid bodies. To test the usefulness of the method in refining atomic structures within cryoEM density we incorporated it into our flexible fitting protocol (Flex-EM). Our benchmark includes 13 pairs of protein structures in two conformations each, one of which is represented by a corresponding cryoEM map. Refining the structures in simulated and experimental maps at the 5–15 Å resolution range using rigid bodies identified by RIBFIND shows a significant improvement over using individual SSEs as rigid bodies. For the 15 Å resolution simulated maps, using RIBFIND-based rigid bodies improves the initial fits by 40.64% on average, as compared to 26.52% when using individual SSEs. Furthermore, for some test cases we show that at the sub-nanometer resolution range the fits can be further improved by applying a two-stage refinement protocol (using RIBFIND-based refinement followed by an SSE-based refinement). The method is stand-alone and could serve as a general interactive tool for guiding flexible fitting into EM maps.     

Molding atomic structures into intermediate-resolution cryo-EM density maps of ribosomal complexes using real-space refinement

Real-space refinement has been previously introduced as a flexible fitting method to interpret medium-resolution cryo-EM density maps in terms of atomic structures. In this way, conformational changes related to functional processes can be analyzed on the molecular level. In the application of the technique to the ribosome, quasiatomic models have been derived that have advanced our understanding of translocation. In this article, the choice of parameters for the fitting procedure is discussed. The quality of the fitting depends critically on the number of rigid pieces into which the model is divided. Suitable quality indicators are crosscorrelation, R factor, and density residual, all of which can also be locally applied. The example of the ribosome may provide some guidelines for general applications of real-space refinement to flexible fitting problems.     

Smart de novo Macromolecular Structure Modeling from Cryo-EM Maps

The study of macromolecular structures has expanded our understanding of the amazing cell machinery and such knowledge has changed how the pharmaceutical industry develops new vaccines in recent years. Traditionally, X-ray crystallography has been the main method for structure determination, however, cryogenic electron microscopy (cryo-EM) has increasingly become more popular due to recent advancements in hardware and software. The number of cryo-EM maps deposited in the EMDataResource (formerly EMDatabase) since 2002 has been dramatically increasing and it continues to do so. De novo macromolecular complex modeling is a labor-intensive process, therefore, it is highly desirable to develop software that can automate this process. Here we discuss our automated, data-driven, and artificial intelligence approaches including map processing, feature extraction, modeling building, and target identification. Recently, we have enabled DNA/RNA modeling in our deep learning-based prediction tool, DeepTracer. We have also developed DeepTracer-ID, a tool that can identify proteins solely based on the cryo-EM map. In this paper, we will present our accumulated experiences in developing deep learning-based methods surrounding macromolecule modeling applications.     

Cryo-EM Data Are Superior to Contact and Interface Information in Integrative Modeling

Protein-protein interactions carry out a large variety of essential cellular processes. Cryo-electron microscopy (cryo-EM) is a powerful technique for the modeling of protein-protein interactions at a wide range of resolutions, and recent developments have caused a revolution in the field. At low resolution, cryo-EM maps can drive integrative modeling of the interaction, assembling existing structures into the map. Other experimental techniques can provide information on the interface or on the contacts between the monomers in the complex. This inevitably raises the question regarding which type of data is best suited to drive integrative modeling approaches. Systematic comparison of the prediction accuracy and specificity of the different integrative modeling paradigms is unavailable to date. Here, we compare EM-driven, interface-driven, and contact-driven integrative modeling paradigms. Models were generated for the protein docking benchmark using the ATTRACT docking engine and evaluated using the CAPRI two-star criterion. At 20 Å resolution, EM-driven modeling achieved a success rate of 100%, outperforming the other paradigms even with perfect interface and contact information. Therefore, even very low resolution cryo-EM data is superior in predicting heterodimeric and heterotrimeric protein assemblies. Our study demonstrates that a force field is not necessary, cryo-EM data alone is sufficient to accurately guide the monomers into place. The resulting rigid models successfully identify regions of conformational change, opening up perspectives for targeted flexible remodeling.     

Flexible fitting to cryo-electron microscopy maps with coarse-grained elastic network models

Cryo-electron microscopy has become an important tool for protein structure determination in recent decades. Since proteins may exist in multiple conformational states, combining high resolution X-ray or NMR structures with cryo-electron microscopy maps is a useful approach to obtain proteins in different functional states. Flexible fitting methods used in cryo-electron microscopy aim to obtain an unknown protein conformation from a high resolution structure and a cryo-electron microscopy map. Since all-atom flexible fitting is computationally expensive, many efficient flexible fitting algorithms that utilize coarse-grained elastic network models have been proposed. In this study, we investigated performance of three coarse-grained elastic network model-based flexible fitting methods (EMFF, iModFit, NMFF) using 25 protein pairs at four resolutions. This study shows that the application of coarse-grained elastic network models to flexible fitting of cryo-electron microscopy maps can provide fast and fruitful models of various conformational states of proteins.     

Biased coarse-grained molecular dynamics simulation approach for flexible fitting of X-ray structure into cryo electron microscopy maps

Several approaches have been introduced to interpret, in terms of high-resolution structure, low-resolution structural data as obtained from cryo-EM. As conformational changes are often observed in biological molecules, these techniques need to take into account the flexibility of proteins. Flexibility has been described in terms of movement between rigid domains and between rigid secondary structure elements, which present some limitations for studying dynamical properties. Normal mode analysis has also been used, but is limited to medium resolution data. All-atom molecular dynamics fitting techniques are more appropriate to fit structures into higher-resolution data as full protein flexibility is considered, but are cumbersome in terms of computational time. Here, we introduce a coarse-grained approach; a Go-model was used to represent biological molecules, combined with biased molecular dynamics to reproduce accurately conformational transitions. Illustrative examples on simulated data are shown. Accurate fittings can be obtained for resolution ranging from 5 to 20 Å. The approach was also tested on experimental data of Elongation Factor G and Escherichia coli RNA polymerase, where its validity is compared to previous models obtained from different techniques. This comparison demonstrates that quantitative flexible techniques, as opposed to manual docking, need to be considered to interpret low-resolution data.     

Applications of the molecular dynamics flexible fitting method

In recent years, cryo-electron microscopy (cryo-EM) has established itself as a key method in structural biology, permitting the structural characterization of large biomolecular complexes in various functional states. The data obtained through single-particle cryo-EM has recently seen a leap in resolution thanks to landmark advances in experimental and computational techniques, resulting in sub-nanometer resolution structures being obtained routinely. The remaining gap between these data and revealing the mechanisms of molecular function can be closed through hybrid modeling tools that incorporate known atomic structures into the cryo-EM data. One such tool, molecular dynamics flexible fitting (MDFF), uses molecular dynamics simulations to combine structures from X-ray crystallography with cryo-EM density maps to derive atomic models of large biomolecular complexes. The structures furnished by MDFF can be used subsequently in computational investigations aimed at revealing the dynamics of the complexes under study. In the present work, recent applications of MDFF are presented, including the interpretation of cryo-EM data of the ribosome at different stages of translation and the structure of a membrane-curvature-inducing photosynthetic complex.     

How different are structurally flexible and rigid binding sites? Sequence and structural features discriminating proteins that do and do not undergo conformational change upon ligand binding

Proteins are dynamic molecules and often undergo conformational change upon ligand binding. It is widely accepted that flexible loop regions have a critical functional role in enzymes. Lack of consideration of binding site flexibility has led to failures in predicting protein functions and in successfully docking ligands with protein receptors. Here we address the question: which sequence and structural features distinguish the structurally flexible and rigid binding sites? We analyze high-resolution crystal structures of ligand bound (holo) and free (apo) forms of 41 proteins where no conformational change takes place upon ligand binding, 35 examples with moderate conformational change, and 22 cases where a large conformational change has been observed. We find that the number of residue-residue contacts observed per-residue (contact density) does not distinguish flexible and rigid binding sites, suggesting a role for specific interactions and amino acids in modulating the conformational changes. Examination of hydrogen bonding and hydrophobic interactions reveals that cases that do not undergo conformational change have high polar interactions constituting the binding pockets. Intriguingly, the large, aromatic amino acid tryptophan has a high propensity to occur at the binding sites of examples where a large conformational change has been noted. Further, in large conformational change examples, hydrophobic-hydrophobic, aromatic-aromatic, and hydrophobic-polar residue pair interactions are dominant. Further analysis of the Ramachandran dihedral angles (phi, psi) reveals that the residues adopting disallowed conformations are found in both rigid and flexible cases. More importantly, the binding site residues adopting disallowed conformations clustered narrowly into two specific regions of the L-Ala Ramachandran map. Examination of the dihedral angles changes upon ligand binding shows that the magnitude of phi, psi changes are in general minimal, although some large changes particularly between right-handed alpha-helical and extended conformations are seen. Our work further provides an account of conformational changes in the dihedral angles space. The findings reported here are expected to assist in providing a framework for predicting protein-ligand complexes and for template-based prediction of protein function.     

FLIPDock: docking flexible ligands into flexible receptors

Conformational changes of biological macromolecules when binding with ligands have long been observed and remain a challenge for automated docking methods. Here we present a novel protein-ligand docking software called FLIPDock (Flexible LIgand-Protein Docking) allowing the automated docking of flexible ligand molecules into active sites of flexible receptor molecules. In FLIPDock, conformational spaces of molecules are encoded using a data structure that we have developed recently called the Flexibility Tree (FT). While the FT can represent fully flexible ligands, it was initially designed as a hierarchical and multiresolution data structure for the selective encoding of conformational subspaces of large biological macromolecules. These conformational subspaces can be built to span a range of conformations important for the biological activity of a protein. A variety of motions can be combined, ranging from domains moving as rigid bodies or backbone atoms undergoing normal mode-based deformations, to side chains assuming rotameric conformations. In addition, these conformational subspaces are parameterized by a small number of variables which can be searched during the docking process, thus effectively modeling the conformational changes in a flexible receptor. FLIPDock searches the variables using genetic algorithm-based search techniques and evaluates putative docking complexes with a scoring function based on the AutoDock3.05 force-field. In this paper, we describe the concepts behind FLIPDock and the overall architecture of the program. We demonstrate FLIPDock's ability to solve docking problems in which the assumption of a rigid receptor previously prevented the successful docking of known ligands. In particular, we repeat an earlier cross docking experiment and demonstrate an increased success rate of 93.5%, compared to original 72% success rate achieved by AutoDock over the 400 cross-docking calculations. We also demonstrate FLIPDock's ability to handle conformational changes involving backbone motion by docking balanol to an adenosine-binding pocket of protein kinase A.     

Computational prediction of atomic structures of helical membrane proteins aided by EM maps

Integral membrane proteins pose a major challenge for protein-structure prediction because only approximately 100 high-resolution structures are available currently, thereby impeding the development of rules or empirical potentials to predict the packing of transmembrane alpha-helices. However, when an intermediate-resolution electron microscopy (EM) map is available, it can be used to provide restraints which, in combination with a suitable computational protocol, make structure prediction feasible. In this work we present such a protocol, which proceeds in three stages: 1), generation of an ensemble of alpha-helices by flexible fitting into each of the density rods in the low-resolution EM map, spanning a range of rotational angles around the main helical axes and translational shifts along the density rods; 2), fast optimization of side chains and scoring of the resulting conformations; and 3), refinement of the lowest-scoring conformations with internal coordinate mechanics, by optimizing the van der Waals, electrostatics, hydrogen bonding, torsional, and solvation energy contributions. In addition, our method implements a penalty term through a so-called tethering map, derived from the EM map, which restrains the positions of the alpha-helices. The protocol was validated on three test cases: GpA, KcsA, and MscL.     

Discrete analyses of protein dynamics

Abstract

Protein structures are highly dynamic macromolecules. This dynamics is often analysed through experimental and/or computational methods only for an isolated or a limited number of proteins. Here, we explore large-scale protein dynamics simulation to observe dynamics of local protein conformations using different perspectives. We analysed molecular dynamics to investigate protein flexibility locally, using classical approaches such as RMSf, solvent accessibility, but also innovative approaches such as local entropy. First, we focussed on classical secondary structures and analysed specifically how β-strand, β–turns, and bends evolve during molecular simulations. We underlined interesting specific bias between β–turns and bends, which are considered as the same category, while their dynamics show differences. Second, we used a structural alphabet that is able to approximate every part of the protein structures conformations, namely protein blocks (PBs) to analyse (i) how each initial local protein conformations evolve during dynamics and (ii) if some exchange can exist among these PBs. Interestingly, the results are largely complex than simple regular/rigid and coil/flexible exchange. Abbreviations N_eq number of equivalent

PB Protein Blocks

PDB Protein DataBank

RMSf root mean square fluctuations

Communicated by Ramaswamy H. Sarma     

Testing a flexible-receptor docking algorithm in a model binding site

Sampling receptor flexibility is challenging for database docking. We consider a method that treats multiple flexible regions of the binding site independently, recombining them to generate different discrete conformations. This algorithm scales linearly rather than exponentially with the receptor's degrees of freedom. The method was first evaluated for its ability to identify known ligands of a hydrophobic cavity mutant of T4 lysozyme (L99A). Some 200000 molecules of the Available Chemical Directory (ACD) were docked against an ensemble of cavity conformations. Surprisingly, the enrichment of known ligands from among a much larger number of decoys in the ACD was worse than simply docking to the apo conformation alone. Large decoys, accommodated in the larger cavity conformations sampled in the ensemble, were ranked better than known small ligands. The calculation was redone with an energy correction term that considered the cost of forming the larger cavity conformations. Enrichment improved, as did the balance between high-ranking large and small ligands. In a second retrospective test, the ACD was docked against a conformational ensemble of thymidylate synthase. Compared to docking against individual enzyme conformations, the flexible receptor docking approach improved enrichment of known ligands. Including a receptor conformational energy weighting term improved enrichment further. To test the method prospectively, the ACD database was docked against another cavity mutant of lysozyme (L99A/M102Q). A total of 18 new compounds predicted to bind this polar cavity and to change its conformation were tested experimentally; 14 were found to bind. The bound structures for seven ligands were determined by X-ray crystallography. The predicted geometries of these ligands all corresponded to the observed geometries to within 0.7A RMSD or better. Significant conformational changes of the cavity were observed in all seven complexes. In five structures, part of the observed accommodations were correctly predicted; in two structures, the receptor conformational changes were unanticipated and thus never sampled. These results suggest that although sampling receptor flexibility can lead to novel ligands that would have been missed when docking a rigid structure, it is also important to consider receptor conformational energy.     

Constructing and validating initial Cα models from subnanometer resolution density maps with pathwalking

A significant number of macromolecular structures solved by electron cryo-microscopy and X-ray crystallography obtain resolutions of 3.5-6?, at which direct atomistic interpretation is difficult. To address this, we developed pathwalking, a semi-automated protocol to enumerate reasonable Cα models from near-atomic resolution density maps without a structural template or sequence-structure correspondence. Pathwalking uses an approach derived from the Traveling Salesman Problem to rapidly generate an ensemble of initial models for individual proteins, which can later be optimized to produce full atomic models. Pathwalking can also be used to validate and identify potential structural ambiguities in models generated from near-atomic resolution density maps. In this work, examples from the EMDB and PDB are used to assess the broad applicability and accuracy of our method. With the growing number of near-atomic resolution density maps from cryo-EM and X-ray crystallography, pathwalking can become an important tool in modeling protein structures.     

Modeling the third loop of short-chain snake venom neurotoxins: roles of the short-range and long-range interactions

The influence of long-range interactions on local structures is an important issue in understanding protein folding process and protein structure stability. Using short-chain snake venom neurotoxin as a model system, we have studied the conformational properties of eight different loop III sequences either in the environment of one of the short-chain neurotoxin, erabutoxin b (PDB ID 1nxb), or in free state by Monte Carlo simulated annealing method. The surrounding protein structure was found to be crucial in stabilizing the loop conformation. Although all the eight peptides prefer type V beta turn in solution, three of them (KPGI, KPGV, KSGI) turn to type II beta turn and the other five (KKGI, KKGV, KNGI, KQGI, and KRGV) are confined to more rigid type V beta turn conformation in the protein structure. Using flexible tetra-glycine-peptide to screen the backbone conformational space in the protein environment also validates the results. This study shows that long-range interactions do contribute to the stability and the types of conformation for a surface loop in protein, while short-range interactions may only provide candidate conformations, which then have to be filtered by the long-range interactions further.